Linear Equations in Two variables
Telangana Board · Class 9 · Mathematics
Quick revision notes for Linear Equations in Two variables — Telangana Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Introduction to Linear Equations in Two Variables
- A linear equation in two variables has the general form ax + by + c = 0, where a, b, c are real numbers and a, b are not both zero
- Unlike linear equations in one variable (which have unique solutions), linear equations in two variables have infinitely many solutions
- Each solution is represented as an ordered pair (x, y)
Finding Solutions - Step by Step Method
- To find solutions, choose a value for one variable and calculate the corresponding value of the other
- Common approach: Set x = 0 to find y-intercept, set y = 0 to find x-intercept
- Any point (x, y) that satisfies the equation is a solution
Graphical Representation - Complete Method
- The graph of a linear equation in two variables is always a straight line
- Every point on the line represents a solution of the equation
- Every solution of the equation represents a point on the line
Special Cases - Lines Parallel to Axes
- Equation x = k represents a line parallel to y-axis at distance |k| from y-axis
- Equation y = k represents a line parallel to x-axis at distance |k| from x-axis
- Equation of x-axis is y = 0
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